a Mathematics and Physics College, Yangzhou University, Yangzhou 225009, China; b Academy of Meteorological Sciences, Beijing 100081 China; c Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China; d Department of Meteorological Sciences, Lanzhou University, Lanzhou 730000 China
Abstract In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p>3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally.
Received: 06 April 2001
Revised: 02 July 2001
Accepted manuscript online:
PACS:
02.60.Lj
(Ordinary and partial differential equations; boundary value problems)
Fund: Project supported by the National Key Program for Developing Basic Sciences (Grant Nos. G1998040901-1 and G1999043400) and the National Natural Science Foundation of China (Grant No. 49875025).
Cite this article:
Feng Guo-lin (封国林), Cao Hong-xing (曹鸿兴), Dong Wen-jie (董文杰), Chou Ji-fan (丑纪范) A NEW DIFFERENCE SCHEME WITH MULTI-TIME LEVELS 2001 Chinese Physics 10 1004
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